isosurfaces over simplicial partitions of multiresolution grids josiah manson and scott schaefer...
TRANSCRIPT
![Page 1: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/1.jpg)
Isosurfaces Over Simplicial Partitions of Multiresolution Grids
Josiah Manson and Scott SchaeferTexas A&M University
![Page 2: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/2.jpg)
Motivation: Uses of Isosurfaces
![Page 3: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/3.jpg)
Motivation: Goals
• Sharp features• Thin features• Arbitrary octrees• Manifold / Intersection-free
![Page 4: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/4.jpg)
Motivation: Goals
• Sharp features• Thin features• Arbitrary octrees• Manifold / Intersection-free
![Page 5: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/5.jpg)
Motivation: Goals
• Sharp features• Thin features• Arbitrary octrees• Manifold / Intersection-free
Octree Textures on the GPU [Lefebvre et al. 2005]
![Page 6: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/6.jpg)
Motivation: Goals
• Sharp features• Thin features• Arbitrary octrees• Manifold / Intersection-free
![Page 7: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/7.jpg)
Related Work
• Dual Contouring [Ju et al. 2002] • Intersection-free Contouring on an Octree
Grid [Ju 2006]• Dual Marching Cubes [Schaefer and Warren
2004]• Cubical Marching Squares [Ho et al. 2005]• Unconstrained Isosurface Extraction on
Arbitrary Octrees [Kazhdan et al. 2007]
![Page 8: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/8.jpg)
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Dual Contouring+
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![Page 11: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/11.jpg)
Dual Contouring
![Page 12: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/12.jpg)
Dual Contouring
Dual Contouring [Ju et al. 2002] Our method
![Page 13: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/13.jpg)
Dual Contouring
Dual Contouring [Ju et al. 2002] Our method
![Page 14: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/14.jpg)
Related Work
• Dual Contouring [Ju et al. 2002] • Intersection-free Contouring on an Octree
Grid [Ju 2006]• Dual Marching Cubes [Schaefer and Warren
2004]• Cubical Marching Squares [Ho et al. 2005]• Unconstrained Isosurface Extraction on
Arbitrary Octrees [Kazhdan et al. 2007]
![Page 15: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/15.jpg)
Dual Marching Cubes
![Page 16: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/16.jpg)
Dual Marching Cubes
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Dual Marching Cubes
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![Page 18: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/18.jpg)
Dual Marching Cubes
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![Page 19: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/19.jpg)
Dual Marching Cubes
![Page 20: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/20.jpg)
Dual Marching Cubes
Dual Marching Cubes [Schaefer and Warren 2004]
Our method
![Page 21: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/21.jpg)
Dual Marching Cubes
![Page 22: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/22.jpg)
Related Work
• Dual Contouring [Ju et al. 2002] • Intersection-free Contouring on an Octree
Grid [Ju 2006]• Dual Marching Cubes [Schaefer and Warren
2004]• Cubical Marching Squares [Ho et al. 2005]• Unconstrained Isosurface Extraction on
Arbitrary Octrees [Kazhdan et al. 2007]
![Page 23: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/23.jpg)
Our Method Overview
• Create vertices dual to every minimal edge, face, and cube
• Partition octree into 1-to-1 covering of tetrahedra
• Marching tetrahedra creates manifold surfaces• Improve triangulation while preserving
topology
![Page 24: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/24.jpg)
Terminology
• Cells in Octree– Vertices are 0-cells– Edges are 1-cells– Faces are 2-cells– Cubes are 3-cells
• Dual Vertices– Vertex dual to each m-cell– Constrained to interior of cell
![Page 25: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/25.jpg)
Terminology
• Cells in Octree– Vertices are 0-cells– Edges are 1-cells– Faces are 2-cells– Cubes are 3-cells
• Dual Vertices– Vertex dual to each m-cell– Constrained to interior of cell
![Page 26: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/26.jpg)
Terminology
• Cells in Octree– Vertices are 0-cells– Edges are 1-cells– Faces are 2-cells– Cubes are 3-cells
• Dual Vertices– Vertex dual to each m-cell– Constrained to interior of cell
![Page 27: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/27.jpg)
Terminology
• Cells in Octree– Vertices are 0-cells– Edges are 1-cells– Faces are 2-cells– Cubes are 3-cells
• Dual Vertices– Vertex dual to each m-cell– Constrained to interior of cell
![Page 28: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/28.jpg)
Terminology
• Cells in Octree– Vertices are 0-cells– Edges are 1-cells– Faces are 2-cells– Cubes are 3-cells
• Dual Vertices– Vertex dual to each m-cell– Constrained to interior of cell
![Page 29: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/29.jpg)
Our Partitioning of Space
• Start with vertex
![Page 30: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/30.jpg)
Our Partitioning of Space
• Build edges
![Page 31: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/31.jpg)
Our Partitioning of Space
• Build faces
![Page 32: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/32.jpg)
Our Partitioning of Space
• Build cubes
![Page 33: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/33.jpg)
Minimal Edge (1-Cell)
![Page 34: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/34.jpg)
Minimal Edge (1-Cell)
![Page 35: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/35.jpg)
Minimal Edge (1-Cell)
![Page 36: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/36.jpg)
Minimal Edge (1-Cell)
![Page 37: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/37.jpg)
Building Simplices
![Page 38: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/38.jpg)
Building Simplices
![Page 39: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/39.jpg)
Building Simplices
![Page 40: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/40.jpg)
Building Simplices
![Page 41: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/41.jpg)
Building Simplices
![Page 42: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/42.jpg)
Building Simplices
![Page 43: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/43.jpg)
Building Simplices
![Page 44: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/44.jpg)
Building Simplices
![Page 45: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/45.jpg)
Traversing Tetrahedra
![Page 46: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/46.jpg)
Traversing Tetrahedra
![Page 47: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/47.jpg)
Traversing Tetrahedra
Octree Traversal from DC [Ju et al. 2002]
![Page 48: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/48.jpg)
Finding Features
• Minimize distances to planes
![Page 49: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/49.jpg)
Surfaces from Tetrahedra
![Page 50: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/50.jpg)
Manifold Property
• Vertices are constrained to their dual m-cells• Simplices are guaranteed to not fold back• Tetrahedra share faces• Freedom to move allows reproducing features
![Page 51: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/51.jpg)
Finding Features
![Page 52: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/52.jpg)
Finding Features
![Page 53: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/53.jpg)
Finding Features
![Page 54: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/54.jpg)
Finding Features
![Page 55: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/55.jpg)
Improving Triangulation
![Page 56: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/56.jpg)
Possible Problem: Face
Before After
![Page 57: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/57.jpg)
Possible Problem: Edge
Before After
![Page 58: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/58.jpg)
Preserving Topology
• Only move vertex to surface if there is a single contour.
• Count connected components.
![Page 59: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/59.jpg)
Preserving Topology
• Only move vertex to surface if there is a single contour.
• Count connected components.
![Page 60: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/60.jpg)
Improving Triangulation
Before
After
![Page 61: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/61.jpg)
Results
![Page 62: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/62.jpg)
Results
![Page 63: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/63.jpg)
TimesArmadillo Man Mechanical Part Lens Tank
Depth 8 9 10 8
Ours 2.58s 4.81s 9.72s 8.78s
Ours (Improved Triangles)
2.69s 6.80s 10.35s 8.19s
Dual Marching Cubes 1.85s 3.54s 6.42s 5.29s
Dual Contouring 1.35s 2.97s 5.99s 3.78s
![Page 64: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/64.jpg)
Conclusions
• Calculate isosurfaces over piecewise smooth functions
• Guarantee manifold surfaces• Reproduce sharp and thin features• Improved triangulation
![Page 65: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/65.jpg)
![Page 66: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/66.jpg)
Contour Refinement & Error Metric
![Page 67: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/67.jpg)
Finding Features
![Page 68: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/68.jpg)
Limitations
• Imperfect detection of sharp edges with multiple features
• Cube corners cannot move, limiting triangulation improvements
• Speed
![Page 69: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/69.jpg)
TimesTime Breakdown of TankOurs Ours (Improved Triangles) DMC DC
Total Time 8.78s 8.19s 5.29s 3.78s
Time Tree 4.02s 6.13s 3.41s 2.69s
Time Extract 4.77s 2.06s 1.88s 1.09s
Triangles 3.63M 1.13M 1.16M 727k
![Page 70: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/70.jpg)
Traversing Edges
![Page 71: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/71.jpg)
Traversing Edges
![Page 72: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/72.jpg)
Traversing Edges
![Page 73: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/73.jpg)
Traversing Edges
![Page 74: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/74.jpg)
Traversing Edges
![Page 75: Isosurfaces Over Simplicial Partitions of Multiresolution Grids Josiah Manson and Scott Schaefer Texas A&M University](https://reader036.vdocuments.site/reader036/viewer/2022062421/56649b5b550346318e8daaa0/html5/thumbnails/75.jpg)
Traversing Edges
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Traversing Edges
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